A097075 - OEIS

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A097075

Expansion of (1-x-x^2)/(1-x-3x^2-x^3).

1, 0, 2, 3, 9, 20, 50, 119, 289, 696, 1682, 4059, 9801, 23660, 57122, 137903, 332929, 803760, 1940450, 4684659, 11309769, 27304196, 65918162, 159140519, 384199201, 927538920, 2239277042, 5406093003, 13051463049, 31509019100, 76069501250 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	`Counts closed walks of length n at a vertex of a triangle, to which a loop has been added at one of the other vertices.`
	FORMULA	`a(n)=(1+sqrt(2))^n/4+(1-sqrt(2))^n/4+(-1)^n/2; a(n)=a(n)+3a(n-2)+a(n-3); a(n)=(-1)^n/2+sum{k=0..floor(n/2), binomial(n, 2k)2^k}/2; a(n)=(-1)^n/2+A001333(n)/2.`
	CROSSREFS	`Cf. A000129, A051927, A097076.` `Sequence in context: A106519 A006866 A121908 * A036673 A111189 A001004` `Adjacent sequences: A097072 A097073 A097074 * A097076 A097077 A097078`
	KEYWORD	`easy,nonn`
	AUTHOR	`Paul Barry (pbarry(AT)wit.ie), Jul 22 2004`

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Last modified February 16 16:51 EST 2012. Contains 205938 sequences.